Tut, tut, Tan Elaine. You know that the answer to that question is "Yes". You also know that one of us is going to send you here. So, why don't you just post a sentence where you are not sure which word is appropriate?
Let me try to explain the difference. I believe 'tournament' is for sports events. So for those events not involving sport, for example, chess, I will have to use 'competition'. Or is it a chess contest?
You are more likely to have a chess tournament in which lots of people are playing chess, and a chess competition set by a newspaper or magazine.
'Tournament is restricted to a series of games,matches,or other activities btween teams or individuals, not just sports events, leading to one or more winners.
A competition can be an opportunity to win a prize by doing something more successfully than others, though the competitors very often do not see each other.
Whether a competitive event is called a contest, race, competition or tournament is entirely the decision of the organiser/s of said event.
They can call it whatever they choose — and who's to say them nay?
At worst they put themselves at risk of sounding ridiculous or pretentious by using tournament when another word would sound less grand — 'knitting championship', 'push-a-marble-up-a-hill-with-your-nose contest', 'running up the stairs of the Empire State Building race'* etc.
The reason for this is that there still lurks in the British collective racial memory vague echos of a time when a tournament was a splendid ceremonial display of bravery and fortitude.
* Since you ask, Thomas Dold holds the record – 1576 steps in 10min 8sec.
One team playing one other team is a "competition." A "tournament" involves multiple levels, like having the best 16 teams in the (world/country/region) compete to determine a champion.
You will certainly hear BrE commentators referring to the entire football World Cup as a competition even though there are more than two teams taking part. The format is that of a tournament but it's still a competition (and a contest!)